Locus

Drag the red dot to shift the locus.

Exercises for students
Sketch the following loci on paper and check your answers using the above applet:

| z - 2 | = 2	| z + 2 | = 2	| z - i | = 1	| z + i | = 1
| z - 1 | = | z - i |	| z - 1 | = | z - 1 - 2i |	| z | = | z - 2 |
arg (z - 1) = pi/4	arg (z - 1) = 3pi/4	arg (z - 1) = -pi/4	arg (z - 1) = -3pi/4
arg (z + 1) = pi/4	arg (z + 1) = -pi/4	arg (z - 1 - i) = pi/4	arg (z - 1 - i) = -pi/4

Sketch the locus of the point representing the complex number z in each of the following cases :
(a) | z - 1 - i | = 1
(b) | z + 1 | = | z + i |
(c) arg(z + 1) = pi/2



Summary

The locus of | z - (a + bi) | = r
is a circle with centre at (a, b) and radius r.

The locus of | z - (a + bi) | = | z - (c + di) |
is the perpendicular bisector of the line joining (a, b) and (c, d).

The locus of arg( z - (a + bi) ) = θ
is a half-line starting at (a, b) and making an angle of θ with the positive x-axis.

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